Sure, our speaker doesn't <em>say</em> that she's alone here – but how many times do you lay awake thinking in the middle of the night with someone else? Not very often. It's fair to assume that our speaker starts out alone.
That nobody, But nobody Can make it out here alone. (8-10)
See? Whoever it is that's alone, they're probably not doing so well. The fact that these lines become the refrain of the poem makes it oh-so-clear that isolation is a central theme in this poem.
Alone, all alone Nobody, but nobody Can make it out here alone. (11-13)
Yup. Whoever you are, you can't make it alone. We're so sure of it, we're going to say it three times over the course of three lines. Repetition much? That's what we thought, too.
They've got expensive doctors To cure their hearts of stone. (18-19)
It turns out that our typical methods of fixing problems – like hiring a doctor or a shrink – won't solve this sort of isolation. The heart doctors don't actually address <em>this</em> kind of heart – the metaphorical heart, which deals with all of our caring and loving.
The race of man is suffering (30)
Don't worry. You're not alone. Everyone feels alone. And that's the weird paradox of this poem: everyone is isolated. We're all isolated together.